A nonlift newform in S13(K(16))−

(Filename: eigs/eig-minus-13-16-4.html)

FORMULA FOR THE EIGENFORM  f
with 313−3λ3 = α,
where throughout this wepage, α is taken to have minimal polynomial  -995982194880000 + 47414289600*x - 427176*x^2 + x^3
Note that T(3) is the Hecke operator under the scalar-invariant slash and λ3 is the corresponding eigenvalue.
The eigenform   f  has the formula
    f = Σi=112 bi Grit(φi) + Σi=045 c1,i T(3)i g1 + Σi=045 c3,i T(3)i g3 + Σi=045 c4,i T(3)i g4
where g1, g3, g4 are the Borcherds products that helped span the space S13(K(16))− and where φi are jacobi forms in J13,16cusp given by the following table.
φ1 TB(13;1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,3)|W2
φ2 TB(13;1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,6)|W3
φ3 TB(13;1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,4,4)|W3
φ4 TB(13;1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3)|W3
φ5 TB(13;1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3)|W3
φ6 TB(13;1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,10)|W5
φ7 TB(13;1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,5,9)|W5
φ8 TB(13;1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,5,6,7)|W5
φ9 TB(13;1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,4,4,5,5,6)|W5
φ10 TB(13;1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,3,7,7)|W5
φ11 TB(13;1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,4,4,4,4,5,5)|W5
φ12 TB(13;1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,3,3,3,9)|W5
Here is a table of the coefficients bi and cj,i.
b1 -32073840347666943847824165603347019464020938406572467297250044557420555488416399121357669150938821966593472965539501199711895340004118568805882587282836397429870374583966738324924146332698257927199712908806260920627745616643737090813946972635668733517752665134699481563945409421114931722130298190744800189015673271155538106023883008535656875342397267625612443/13861662769925433382848572194797720184064138489408046656194528278812902360341748694981293089846314305506110190985400517551059308163155747062766792739941289439395308630683616345180314983430825351441805719771514541999501645153931130948661473047546052043877912458800486333537284430511189033271853125030968155072653076311278878720000000000000 + (277563049170971260088353803873888015669589181088107028072432466425414756462295814436060932357416160705063209433661033172242027594021441781179010368522657831166490585818111506870933003279361842256282247006245801170162045437320476828453841479766922196016681674866885481222059819043129728116189262556463257523909581807098943708878093960880017598307307252457221*α)/12475496492932890044563714975317948165657724640467241990575075450931612124307573825483163780861682874955499171886860465795953377346840172356490113465947160495455777767615254710662283485087742816297625147794363087799551480638538017853795325742791446839490121212920437700183555987460070129944667812527871339565387768680150990848000000000000000 - (92367297210999424920797502213167426098160056253173419093443069033346035620917306075622855483795173409204726944152556436512221116265015579902018967375853880015661222503348666314239967823625301504503446669997645726975603994056012438895825678796326344984790436899581972183255378569596528794018281227031898677337139415787086059271923941373963790722823142099*α^2)/1796471494982336166417174956445784535854712348227282846642810864934152145900290630869575584444082333993591880751707907074617286337944984819334576339096391111345631998536596678335368821852634965546858021282388284643135413211949474570946526906961968344886577454660543028826432062194250098712032165004013472897415838689941742682112000000000000000
b2 34800860848236357842897075749453238131483311611220081515283715801946615354004869820899150097545292052133794012860449982716171203144104465861341634992148546208126930868895326950078665756443918622092739711554884883594113593202511467401070997902104409998047554037656853372526063795137921354389810622461479045622904061287105347750600679209508857777290120783315161/93566223696996675334227862314884611242432934803504314929313065881987090932306803691123728356462621562166243789151453493469650330101301292673675850994603703715918333257114410329967126138158071122232188608457723158496636104789035133903464943070935851296175909096903282751376669905950525974585008593959035046740408265101132431360000000000000 - (301159283722451068344023394209340597933709750723941293863247272262867278649458045682794635189178015291122075753860824484425341509454701897395333398078503545837261876849675240389562713436840138629552986174842788825584235159263468900054939888731867399317536047622060676225377652399937912708386349455435966021633765353131084733859800741321374695243672961327367*α)/84209601327297007800805076083396150118189641323153883436381759293788381839076123322011355520816359405949619410236308144122685297091171163406308265895143333344326499931402969296970413524342264010008969747611950842646972494310131620513118448763842266166558318187212954476239002915355473377126507734563131542066367438591019188224000000000000000 + (100218956279260233778314428971719435695523096453409468736538659883253694207002746364845387155398620268735063733088191557691716367722469562467969134026288784178813940620578198378480876816201050053351227598202495576228263288765129503632801932932830301417900310907039029562254122972433509952227706659954435226775671223615546064097608556269187200343670062273*α^2)/12126182591130769123315930956009045617019308350534159214838973338305526984826961758369635194997555754456745195074028372753666682781128647530508390288900640001583015990122027578763739547505286017441291643656120921341164039180658953353889056621993286327984397818958665444578416419811188166306217113777090942057556911157106763104256000000000000000
b3 41436684328477142880621466978632458045605221753808404673158749027849501558730727020642914262285864354725041385605348270123707074842435695964019944733733911123271018217450503692377069429412637302771182159277245896210728746441003220969308105408782427759276144436123366273769524261907577524290873389289264334405926690442110711102183324478677368076228691880147241/103962470774440750371364291460982901380481038670560349921458962091096767702563115212359698173847357291295826432390503881632944811223668102970750945549559670795464814730127122588852362375731190135813542898286359064996262338654483482114961047856595390329084343441003647501529633228833917749538898437732261163044898072334591590400000000000000 - (358584539849907235804868674590803325638530631391946134744497088866173820819968638723752011883550698682221670845624150395796240093356377710172109429137023224739014044503116887389115841367551314969595155615071504772925642528874980762018315028204811275430199477881331156624240716081768969764350503037772685673508383526856326878628290956377451345563404959379127*α)/93566223696996675334227862314884611242432934803504314929313065881987090932306803691123728356462621562166243789151453493469650330101301292673675850994603703715918333257114410329967126138158071122232188608457723158496636104789035133903464943070935851296175909096903282751376669905950525974585008593959035046740408265101132431360000000000000000 + (119328829293897096529281152783101219133845568214297674853632808504258654468858550589242143359180293477186452608693493457831026888566545730459357688183995294088317988269802168892923445242903233106533062435508206679808805082001937314332549086808450532523495783683927790022162715698839978583393887942808974419571994716914214771298943468437731028105902989713*α^2)/13473536212367521248128812173343384018910342611704621349821081487006141094252179731521816883330617504951939105637809303059629647534587386145009322543222933335092239989024475087515266163894762241601435159617912134823515599089621059282098951802214762586649330909954072716198240466456875740340241237530101046730618790174563070115840000000000000000
b4 201533232098194029768905897910999630750571394369685353039721563714193484612856324462827812038372293889509116553313088866531107119204998048881152733699488032269443242850816546698205789773376777230505549987684945416322399445999687449218738106527375357019586972640338521983123735109521665749631916122776068426365653128970776651321667648708755227602565015009963541/233915559242491688335569655787211528106082337008760787323282664704967727330767009227809320891156553905415609472878633733674125825253253231684189627486509259289795833142786025824917815345395177805580471521144307896241590261972587834758662357677339628240439772742258206878441674764876314936462521484897587616851020662752831078400000000000000 - (1744041638612960134159503651513988589350572141443292030102234020140057021267547627596050780634413386228232658922188443708939575592814005146494444565094704325518421047861818419476439928875096980107786626416894169287055896778682770084180922483918038428077978680175389828964922412871337661271539395828611147028796752829575830350809334102597567516066011937585227*α)/210524003318242519502012690208490375295474103307884708590954398234470954597690308305028388802040898514874048525590770360306713242727927908515770664737858333360816249828507423242426033810855660025022424369029877106617431235775329051282796121909605665416395795468032386190597507288388683442816269336407828855165918596477547970560000000000000000 + (580380877614720511285625250107040167354014498517700227872629748678941913052744783984584154919064937383359687644360854817211567343046486258536303448617229104329401499769912023488501183736446250061416018611324062879733548891355382276970328476570580670311033309546820650692903945843568148756959432791683735102412072559445650002199191167578954764753793995613*α^2)/30315456477826922808289827390022614042548270876335398037097433345763817462067404395924087987493889386141862987685070931884166706952821618826270975722251600003957539975305068946909348868763215043603229109140302303352910097951647383384722641554983215819960994547396663611446041049527970415765542784442727355143892277892766907760640000000000000000
b5 698830091452028262744420063792320349682326230947381750859141866181119722197460902240949582294136702887360386526208973558073672436010970051670260772891172304930413149860394205052477615268333507193497824051814595438906237377606489400321610556080263858572007908621485279902203294395130735850854160831472972662742539022908442598073141996673029468535780576949726927/374264894787986701336911449259538444969731739214017259717252263527948363729227214764494913425850486248664975156605813973878601320405205170694703403978414814863673333028457641319868504552632284488928754433830892633986544419156140535613859772283743405184703636387613131005506679623802103898340034375836140186961633060404529725440000000000000 - (6047621823541778926490590337519599833802496648170615343692712392909767435344605553002781533078122392853381276222452397625406239311723735885392406407081502127168935689306972556609709853839720676415982416179380557029465303846093919726218322084963751403120951835678242040405562270907875080478199801297493822123096589110411774057882569364297303337350960886809169*α)/336838405309188031203220304333584600472758565292615533745527037175153527356304493288045422083265437623798477640945232576490741188364684653625233063580573333377305999725611877187881654097369056040035878990447803370587889977240526482052473795055369064666233272748851817904956011661421893508506030938252526168265469754364076752896000000000000000 + (2012531948870650391977911741246460540605353583928050756298636639600268343166578316652519473877947215847191157555093119671538077076885839966843010224477810090146999091476590557842175114447588513135813990276732173013171741651428814009623962490430110874916379419230096394639949925633631048712621194956899004807872272678773844836601467400690471307307562710311*α^2)/48504730364523076493263723824036182468077233402136636859355893353222107939307847033478540779990223017826980780296113491014666731124514590122033561155602560006332063960488110315054958190021144069765166574624483685364656156722635813415556226487973145311937591275834661778313665679244752665224868455108363768230227644628427052417024000000000000000
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c3,250
c3,260
c3,270
c3,280
c3,290
c3,300
c3,310
c3,320
c3,330
c3,340
c3,350
c3,360
c3,370
c3,380
c3,390
c3,400
c3,410
c3,420
c3,430
c3,440
c3,450
c4,00
c4,10
c4,20
c4,30
c4,40
c4,50
c4,60
c4,70
c4,80
c4,90
c4,100
c4,110
c4,120
c4,130
c4,140
c4,150
c4,160
c4,170
c4,180
c4,190
c4,200
c4,210
c4,220
c4,230
c4,240
c4,250
c4,260
c4,270
c4,280
c4,290
c4,300
c4,310
c4,320
c4,330
c4,340
c4,350
c4,360
c4,370
c4,380
c4,390
c4,400
c4,410
c4,420
c4,430
c4,440
c4,450

COEFFICIENTS OF f  (return to top)
Use the notation
    [a b c ]=
 
a b
b c
 
Here is a list of some Fourier coefficients of f.

2udet(2u)a(u, f)
[4 -53 704]71/8388608
[8 -89 992]1552687/8455716864 - (257*α)/652298158080 + α^2/657516543344640
[4 -25 160]15-5036693/135291469824 + (47447*α)/52183852646400 - (151*α^2)/52601323467571200
[12 -109 992]2328989673/135291469824 - (47447*α)/10436770529280 + (151*α^2)/10520264693514240
[6 -13 32]2328989673/135291469824 - (47447*α)/10436770529280 + (151*α^2)/10520264693514240
[6 -19 64]23-116397/939524096 + (257*α)/24159191040 - α^2/24352464568320
[14 -42 128]280
[14 -70 352]28-1/2048
[8 -42 224]280
[8 -106 1408]28-1/2048
[16 -113 800]316942697/45097156608 - (47447*α)/3478923509760 + (151*α^2)/3506754897838080
[8 -113 1600]316942697/45097156608 - (47447*α)/3478923509760 + (151*α^2)/3506754897838080
[14 -47 160]31-807383/939524096 + (257*α)/8053063680 - α^2/8117488189440
[20 -101 512]39374346157/135291469824 - (165559*α)/2087354105856 + (503*α^2)/2104052938702848
[10 -91 832]39132616067/67645734912 - (521917*α)/5218385264640 + (1661*α^2)/5260132346757120
[10 -101 1024]39-132616067/67645734912 + (521917*α)/5218385264640 - (1661*α^2)/5260132346757120
[8 -27 96]3914623087/4227858432 - (31097*α)/326149079040 + (121*α^2)/328758271672320
[24 -73 224]47279171551/22548578304 - (519649*α)/1739461754880 + (1697*α^2)/1753377448919040
[12 -73 448]47-1000568579/135291469824 + (521917*α)/10436770529280 - (1661*α^2)/10520264693514240
[4 9 32]47-279171551/22548578304 + (519649*α)/1739461754880 - (1697*α^2)/1753377448919040
[8 -73 672]47-1000568579/135291469824 + (521917*α)/10436770529280 - (1661*α^2)/10520264693514240
[16 -55 192]47976095/939524096 - (11051*α)/24159191040 + (43*α^2)/24352464568320
[2 4 32]4849663/8257536 - (257*α)/637009920 + α^2/642105999360
[26 76 224]48-49663/8257536 + (257*α)/637009920 - α^2/642105999360
[6 12 32]48-49663/8257536 + (257*α)/637009920 - α^2/642105999360
[14 36 96]4849663/8257536 - (257*α)/637009920 + α^2/642105999360
[2 3 32]55-291933325/45097156608 - (56489*α)/695784701952 + (361*α^2)/701350979567616
[14 -29 64]5563259135/1409286144 - (521917*α)/543581798400 + (1661*α^2)/547930452787200
[14 -99 704]55-63259135/1409286144 + (521917*α)/543581798400 - (1661*α^2)/547930452787200
[8 -35 160]5555225/8388608
[2 2 32]60-52687/2064384 + (257*α)/159252480 - α^2/160526499840
[30 -210 1472]600
[16 -50 160]600
[16 -178 1984]605036693/33030144 - (47447*α)/12740198400 + (151*α^2)/12842119987200
[10 -30 96]605036693/33030144 - (47447*α)/12740198400 + (151*α^2)/12842119987200
[10 -50 256]600
[8 -50 320]60-52687/2064384 + (257*α)/159252480 - α^2/160526499840
[8 -114 1632]600
[2 1 32]63553424581/9663676416 - (9205469*α)/5218385264640 + (4411*α^2)/751447478108160
[16 -225 3168]63-188420099/19327352832 + (3653419*α)/10436770529280 - (1661*α^2)/1502894956216320
[4 33 288]63188420099/19327352832 - (3653419*α)/10436770529280 + (1661*α^2)/1502894956216320
[12 -159 2112]63α/8388608
[8 -97 1184]638715187/402653184 - (455147*α)/217432719360 + (253*α^2)/31310311587840
[2 0 32]640
[2 8 64]640
[2 16 160]640
[4 8 32]640
[20 56 160]640
[10 -24 64]640
[10 -64 416]640
[10 -144 2080]640
[36 -469 6112]71-462210169/6442450944 + (13291121*α)/3478923509760 - (6919*α^2)/500964985405440
[18 -181 1824]71-33350301073/135291469824 + (53567663*α)/10436770529280 - (170479*α^2)/10520264693514240
[18 -235 3072]714675603619/135291469824 - (2675513*α)/2087354105856 + (8185*α^2)/2104052938702848
[12 -85 608]71-33350301073/135291469824 + (53567663*α)/10436770529280 - (170479*α^2)/10520264693514240
[120 277 640]71462210169/6442450944 - (13291121*α)/3478923509760 + (6919*α^2)/500964985405440
[10 -43 192]71-82997739/939524096 + (7967*α)/2684354560 - (31*α^2)/2705829396480
[10 -53 288]71-4675603619/135291469824 + (2675513*α)/2087354105856 - (8185*α^2)/2104052938702848
[40 -441 4864]79-1385035343/15032385536 + (119933*α)/231928233984 - (61*α^2)/233783659855872
[20 -121 736]79444804227/1610612736 - (3653419*α)/869730877440 + (1661*α^2)/125241246351360
[190 441 1024]791385035343/15032385536 - (119933*α)/231928233984 + (61*α^2)/233783659855872
[10 -71 512]79-444804227/1610612736 + (3653419*α)/869730877440 - (1661*α^2)/125241246351360
[10 -121 1472]79-20532293/234881024 + (2827*α)/2013265920 - (11*α^2)/2029372047360
[44 -397 3584]8730332853791/135291469824 - (100302241*α)/10436770529280 + (372833*α^2)/10520264693514240
[22 -45 96]8770209854891/135291469824 - (163360021*α)/10436770529280 + (519893*α^2)/10520264693514240
[22 -243 2688]8712057005735/19327352832 - (31524131*α)/2087354105856 + (14533*α^2)/300578991243264
[16 -115 832]87-70209854891/135291469824 + (163360021*α)/10436770529280 - (519893*α^2)/10520264693514240
[12 -51 224]87951029393/8455716864 - (8314207*α)/652298158080 + (32351*α^2)/657516543344640
[134 307 704]8730332853791/135291469824 - (100302241*α)/10436770529280 + (372833*α^2)/10520264693514240
[46 -138 416]9245750841/66060288 - (158471*α)/5096079360 + (583*α^2)/5136847994880
[46 -230 1152]9212228505/66060288 + (63577*α)/5096079360 - (281*α^2)/5136847994880
[4 6 32]92-12228505/66060288 - (63577*α)/5096079360 + (281*α^2)/5136847994880
[24 -218 1984]92-45750841/66060288 + (158471*α)/5096079360 - (583*α^2)/5136847994880
[26 70 192]9212228505/66060288 + (63577*α)/5096079360 - (281*α^2)/5136847994880
[162 374 864]9245750841/66060288 - (158471*α)/5096079360 + (583*α^2)/5136847994880
[6 26 128]920
[26 -86 288]92-28989673/33030144 + (47447*α)/2548039680 - (151*α^2)/2568423997440
[12 -26 64]92-45750841/66060288 + (158471*α)/5096079360 - (583*α^2)/5136847994880
[12 -38 128]9228989673/33030144 - (47447*α)/2548039680 + (151*α^2)/2568423997440
[12 -122 1248]9212228505/66060288 + (63577*α)/5096079360 - (281*α^2)/5136847994880
[12 -134 1504]920
[48 -337 2368]952582033025/3758096384 - (654643*α)/57982058496 + (1907*α^2)/58445914963968
[24 -337 4736]95-6091272377/7516192768 + (9916423*α)/579820584960 - (31559*α^2)/584459149639680
[4 17 96]9537415982769/135291469824 - (365574091*α)/52183852646400 + (1301003*α^2)/52601323467571200
[16 -81 416]95-37415982769/135291469824 + (365574091*α)/52183852646400 - (1301003*α^2)/52601323467571200
[6 49 416]956091272377/7516192768 - (9916423*α)/579820584960 + (31559*α^2)/584459149639680
[12 -145 1760]95-167028525/469762048 + (14135*α)/805306368 - (55*α^2)/811748818944
[60 145 352]951018002425/135291469824 + (44057893*α)/2087354105856 - (177893*α^2)/2104052938702848
[10 15 32]952582033025/3758096384 - (654643*α)/57982058496 + (1907*α^2)/58445914963968
[52 -261 1312]103-4202512397/45097156608 - (1267753*α)/695784701952 + (233*α^2)/701350979567616
[4 5 32]1034202512397/45097156608 + (1267753*α)/695784701952 - (233*α^2)/701350979567616
[26 -261 2624]103-22429665185/45097156608 + (72546463*α)/3478923509760 - (230879*α^2)/3506754897838080
[14 -59 256]103-20039345/939524096 + (100487*α)/8053063680 - (391*α^2)/8117488189440
[14 -101 736]103-22429665185/45097156608 + (72546463*α)/3478923509760 - (230879*α^2)/3506754897838080
[56 -169 512]111-10256920111/45097156608 - (28435567*α)/3478923509760 + (92591*α^2)/3506754897838080
[28 -169 1024]11159763257833/67645734912 - (127584983*α)/5218385264640 + (406039*α^2)/5260132346757120
[120 297 736]111217620737323/135291469824 - (739571093*α)/10436770529280 + (2636629*α^2)/10520264693514240
[6 9 32]11110256920111/45097156608 + (28435567*α)/3478923509760 - (92591*α^2)/3506754897838080
[14 -169 2048]111744266885/469762048 - (310199*α)/7247757312 + (1207*α^2)/7305739370496
[14 -183 2400]111-156172628527/45097156608 + (46867741*α)/695784701952 - (147677*α^2)/701350979567616
[12 -87 640]111-59763257833/67645734912 + (127584983*α)/5218385264640 - (406039*α^2)/5260132346757120
[10 23 64]111-217620737323/135291469824 + (739571093*α)/10436770529280 - (2636629*α^2)/10520264693514240
[2 4 64]1121/2
[58 172 512]112-1/2
[4 4 32]1121/2
[28 -84 256]1121/2
[28 -140 704]112-1/2
[28 -196 1376]112-1/2
[14 -28 64]1121/2
[14 -84 512]112-1/2
[8 12 32]112-1/2
[16 -84 448]1121/2
[16 -148 1376]112-1/2
[16 -212 2816]1121/2
[2 3 64]1196782369725/19327352832 + (111766123*α)/10436770529280 - (61757*α^2)/1502894956216320
[30 -61 128]119-13610891239/19327352832 + (281313263*α)/10436770529280 - (127897*α^2)/1502894956216320
[30 -451 6784]119-6782369725/19327352832 - (111766123*α)/10436770529280 + (61757*α^2)/1502894956216320
[20 -61 192]1191029001021/3221225472 + (2470703*α)/347892350976 - (2137*α^2)/50096498540544
[90 221 544]11945194431247/19327352832 - (315267031*α)/10436770529280 + (132209*α^2)/1502894956216320
[16 -67 288]11955135539/134217728 + (336413*α)/8053063680 - (187*α^2)/1159641169920
[8 67 576]119-13610891239/19327352832 + (281313263*α)/10436770529280 - (127897*α^2)/1502894956216320
[12 -61 320]1191029001021/3221225472 + (2470703*α)/347892350976 - (2137*α^2)/50096498540544
[24 61 160]119-1187930399/9663676416 - (400218521*α)/5218385264640 + (240799*α^2)/751447478108160
[12 -125 1312]119-45194431247/19327352832 + (315267031*α)/10436770529280 - (132209*α^2)/1502894956216320
[2 2 64]124-31811687/22020096 + (63577*α)/1698693120 - (281*α^2)/1712282664960
[62 -434 3040]12445697081/22020096 - (158471*α)/1698693120 + (583*α^2)/1712282664960
[4 2 32]124-31811687/22020096 + (63577*α)/1698693120 - (281*α^2)/1712282664960
[32 -226 1600]124-45697081/22020096 + (158471*α)/1698693120 - (583*α^2)/1712282664960
[16 -98 608]124-31811687/22020096 + (63577*α)/1698693120 - (281*α^2)/1712282664960
[16 -226 3200]124-45697081/22020096 + (158471*α)/1698693120 - (583*α^2)/1712282664960
[8 34 160]1240
[28 -94 320]1246942697/11010048 - (47447*α)/849346560 + (151*α^2)/856141332480
[10 14 32]12445697081/22020096 - (158471*α)/1698693120 + (583*α^2)/1712282664960
[14 -46 160]124-6942697/11010048 + (47447*α)/849346560 - (151*α^2)/856141332480
[14 -130 1216]124-31811687/22020096 + (63577*α)/1698693120 - (281*α^2)/1712282664960
[14 -158 1792]1240
[2 1 64]12755815934141/45097156608 - (33081319*α)/695784701952 + (95015*α^2)/701350979567616
[4 1 32]12755815934141/45097156608 - (33081319*α)/695784701952 + (95015*α^2)/701350979567616
[32 -449 6304]12716861167401/45097156608 - (37056107*α)/695784701952 + (117931*α^2)/701350979567616
[16 -193 2336]12754887031/939524096 - (460801*α)/8053063680 + (1793*α^2)/8117488189440
[8 65 544]127-16861167401/45097156608 + (37056107*α)/695784701952 - (117931*α^2)/701350979567616
[2 0 64]1280
[2 8 96]12821575129/4128768 - (51559*α)/318504960 + (167*α^2)/321052999680
[2 16 192]1280
[4 0 32]1280
[4 16 96]128-21575129/4128768 + (51559*α)/318504960 - (167*α^2)/321052999680
[4 32 288]1280
[6 8 32]12821575129/4128768 - (51559*α)/318504960 + (167*α^2)/321052999680
[22 -112 576]12821575129/4128768 - (51559*α)/318504960 + (167*α^2)/321052999680
[22 -200 1824]12821575129/4128768 - (51559*α)/318504960 + (167*α^2)/321052999680
[22 -288 3776]12821575129/4128768 - (51559*α)/318504960 + (167*α^2)/321052999680
[18 -40 96]12821575129/4128768 - (51559*α)/318504960 + (167*α^2)/321052999680
[18 -112 704]1280
[18 -256 3648]1280
[12 16 32]1280
[12 -64 352]128-21575129/4128768 + (51559*α)/318504960 - (167*α^2)/321052999680
[12 -112 1056]1280
[68 -885 11520]135-14980531133/33822867456 - (30005117*α)/2609192632320 + (207421*α^2)/2630066173378560
[34 -171 864]135282785841239/67645734912 - (3865312781*α)/26091926323200 + (11444173*α^2)/26300661733785600
[34 -341 3424]135105335079317/15032385536 - (947469143*α)/5798205849600 + (3015319*α^2)/5844591496396800
[24 -267 2976]135121907740319/15032385536 - (1315886501*α)/5798205849600 + (4466533*α^2)/5844591496396800
[8 11 32]135-14980531133/33822867456 - (30005117*α)/2609192632320 + (207421*α^2)/2630066173378560
[18 -75 320]135399825341/2818572288 - (21547651*α)/217432719360 + (83843*α^2)/219172181114880
[16 -117 864]135105335079317/15032385536 - (947469143*α)/5798205849600 + (3015319*α^2)/5844591496396800
[12 -75 480]135-7446494117/1879048192 + (24450427*α)/144955146240 - (85691*α^2)/146114787409920
[72 -793 8736]143-85934820077/22548578304 + (114717907*α)/1739461754880 - (416531*α^2)/1753377448919040
[36 -217 1312]143-831218022659/135291469824 + (2806347709*α)/10436770529280 - (8931197*α^2)/10520264693514240
[42 121 352]143-13157978037/3758096384 + (12104975*α)/57982058496 - (48463*α^2)/58445914963968
[6 7 32]143-85934820077/22548578304 + (114717907*α)/1739461754880 - (416531*α^2)/1753377448919040
[6 25 128]143-356908064605/135291469824 - (11283257*α)/2087354105856 + (192505*α^2)/2104052938702848
[18 -199 2208]143-356908064605/135291469824 - (11283257*α)/2087354105856 + (192505*α^2)/2104052938702848
[18 -217 2624]143-2878412175/939524096 + (7511339*α)/24159191040 - (29227*α^2)/24352464568320
[12 -25 64]14313157978037/3758096384 - (12104975*α)/57982058496 + (48463*α^2)/58445914963968
[14 -89 576]14319605956921/19327352832 - (260056369*α)/10436770529280 + (161351*α^2)/1502894956216320
[14 -103 768]143831218022659/135291469824 - (2806347709*α)/10436770529280 + (8931197*α^2)/10520264693514240
[76 -685 6176]151-242399872367/45097156608 + (794787409*α)/3478923509760 - (2899217*α^2)/3506754897838080
[38 -77 160]151-33411514629/2147483648 + (105949151*α)/386547056640 - (48169*α^2)/55662776156160
[38 -115 352]15115846324805/3758096384 - (1577407*α)/57982058496 - α^2/58445914963968
[20 -83 352]151-870995417/939524096 + (81983*α)/8053063680 - (319*α^2)/8117488189440
[8 19 64]151-15846324805/3758096384 + (1577407*α)/57982058496 + α^2/58445914963968
[10 13 32]151242399872367/45097156608 - (794787409*α)/3478923509760 + (2899217*α^2)/3506754897838080
[10 83 704]151-33411514629/2147483648 + (105949151*α)/386547056640 - (48169*α^2)/55662776156160
[78 -234 704]156-280761647/22020096 + (607633*α)/1698693120 - (2129*α^2)/1712282664960
[78 -390 1952]15693592627/66060288 - (167309*α)/5096079360 + (1357*α^2)/5136847994880
[40 -202 1024]156132616067/16515072 - (521917*α)/1274019840 + (1661*α^2)/1284211998720
[40 -522 6816]1560
[6 6 32]156-93592627/66060288 + (167309*α)/5096079360 - (1357*α^2)/5136847994880
[26 -182 1280]156-280761647/22020096 + (607633*α)/1698693120 - (2129*α^2)/1712282664960
[8 10 32]156280761647/22020096 - (607633*α)/1698693120 + (2129*α^2)/1712282664960
[20 -42 96]156280761647/22020096 - (607633*α)/1698693120 + (2129*α^2)/1712282664960
[20 -182 1664]156-93592627/66060288 + (167309*α)/5096079360 - (1357*α^2)/5136847994880
[20 -202 2048]15693592627/66060288 - (167309*α)/5096079360 + (1357*α^2)/5136847994880
[10 22 64]1560
[82 198 480]156-132616067/16515072 + (521917*α)/1274019840 - (1661*α^2)/1284211998720
[10 42 192]1560
[30 -102 352]156132616067/16515072 - (521917*α)/1274019840 + (1661*α^2)/1284211998720
[16 -54 192]156-132616067/16515072 + (521917*α)/1274019840 - (1661*α^2)/1284211998720
[16 -182 2080]1560
[80 -561 3936]15928062010717/2818572288 - (20544947*α)/217432719360 + (66931*α^2)/219172181114880
[40 -561 7872]159201016818805/22548578304 - (97598479*α)/347892350976 + (310607*α^2)/350675489783808
[46 -143 448]15996838744123/7516192768 - (248891909*α)/579820584960 + (853957*α^2)/584459149639680
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[32 -100 320]24052687/2016 - (257*α)/155520 + α^2/156764160
[32 -228 1632]240-52687/2016 + (257*α)/155520 - α^2/156764160
[32 -356 3968]24052687/2016 - (257*α)/155520 + α^2/156764160
[10 20 64]240-5036693/32256 + (47447*α)/12441600 - (151*α^2)/12541132800
[34 92 256]2405036693/32256 - (47447*α)/12441600 + (151*α^2)/12541132800
[12 12 32]240-52687/2016 + (257*α)/155520 - α^2/156764160
[20 -60 192]240-52687/2016 + (257*α)/155520 - α^2/156764160
[20 -100 512]24052687/2016 - (257*α)/155520 + α^2/156764160
[20 -140 992]24052687/2016 - (257*α)/155520 + α^2/156764160
[16 -36 96]2405036693/32256 - (47447*α)/12441600 + (151*α^2)/12541132800
[16 -100 640]240-5036693/32256 + (47447*α)/12441600 - (151*α^2)/12541132800
[16 -164 1696]2405036693/32256 - (47447*α)/12441600 + (151*α^2)/12541132800
[16 -228 3264]240-5036693/32256 + (47447*α)/12441600 - (151*α^2)/12541132800
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[62 -931 13984]247-14190862073545/45097156608 + (16901693303*α)/3478923509760 - (43173559*α^2)/3506754897838080
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[126 -882 6176]252-344260093/4718592 - (1718059*α)/2548039680 + (1661*α^2)/366917713920
[4 2 64]252-188420099/4718592 + (3653419*α)/2548039680 - (1661*α^2)/366917713920
[64 -450 3168]2520
[42 -126 384]2520
[42 -210 1056]252-α/2048
[8 2 32]252-762589069/4718592 + (20128997*α)/2548039680 - (10483*α^2)/366917713920
[32 -194 1184]252-762589069/4718592 + (20128997*α)/2548039680 - (10483*α^2)/366917713920
[32 -450 6336]252344260093/4718592 + (1718059*α)/2548039680 - (1661*α^2)/366917713920
[8 66 576]252-344260093/4718592 - (1718059*α)/2548039680 + (1661*α^2)/366917713920
[24 -126 672]2520
[24 -318 4224]252-α/2048
[14 14 32]252-344260093/4718592 - (1718059*α)/2548039680 + (1661*α^2)/366917713920
[18 -126 896]252762589069/4718592 - (20128997*α)/2548039680 + (10483*α^2)/366917713920
[16 -66 288]2520
[16 -194 2368]252188420099/4718592 - (3653419*α)/2548039680 + (1661*α^2)/366917713920
[18 -78 352]252188420099/4718592 - (3653419*α)/2548039680 + (1661*α^2)/366917713920
[18 -114 736]252-188420099/4718592 + (3653419*α)/2548039680 - (1661*α^2)/366917713920
[18 -222 2752]2520
[18 -258 3712]2520
[2 1 128]25510828854457475/135291469824 + (2080654375*α)/2087354105856 - (10907495*α^2)/2104052938702848
[4 1 64]255-3201901808333/8455716864 + (8134523827*α)/652298158080 - (27584051*α^2)/657516543344640
[64 -897 12576]255-770495354569/6442450944 + (95686697029*α)/17394617548800 - (43503251*α^2)/2504824927027200
[44 -575 7520]25561967565311/528482304 - (797943761*α)/203843174400 + (3061213*α^2)/205473919795200
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[32 -385 4640]255-134574965225/8455716864 - (269851285*α)/130459631616 + (1050005*α^2)/131503308668928
[28 -257 2368]255292720189725/15032385536 - (18515599*α)/25769803776 + (25925*α^2)/8658654068736
[22 -223 2272]255-292720189725/15032385536 + (18515599*α)/25769803776 - (25925*α^2)/8658654068736
[22 -289 3808]2556140588294875/67645734912 - (8478954337*α)/1043677052928 + (30227489*α^2)/1052026469351424
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[2 0 128]2560
[2 8 160]25610646815/49152 - (183143*α)/26542080 + (97*α^2)/3822059520
[2 16 256]2560
[4 0 64]2560
[4 16 128]2560
[4 32 320]2560
[8 0 32]2560
[8 16 64]2560
[40 112 320]2560
[8 32 160]256-10646815/49152 + (183143*α)/26542080 - (97*α^2)/3822059520
[8 64 544]2560
[34 -72 160]25610646815/49152 - (183143*α)/26542080 + (97*α^2)/3822059520
[34 -208 1280]2560
[34 -480 6784]2560
[26 -80 256]256-10646815/49152 + (183143*α)/26542080 - (97*α^2)/3822059520
[26 -184 1312]256-10646815/49152 + (183143*α)/26542080 - (97*α^2)/3822059520
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[26 -392 5920]256-10646815/49152 + (183143*α)/26542080 - (97*α^2)/3822059520
[16 16 32]2560
[16 -48 160]256-10646815/49152 + (183143*α)/26542080 - (97*α^2)/3822059520
[16 -112 800]2560
[20 -48 128]2560
[20 -128 832]2560
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[34 -409 4928]2717745583849/939524096 - (12927871*α)/8053063680 + (50303*α^2)/8117488189440
[28 -423 6400]271-361189337855/7516192768 + (181391083*α)/193273528320 - (576299*α^2)/194819716546560
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[140 -1261 11360]279-19758072635963/135291469824 + (88791440773*α)/10436770529280 - (340140869*α^2)/10520264693514240
[70 -141 288]279-10875992359319/135291469824 + (23630836009*α)/10436770529280 - (75205097*α^2)/10520264693514240
[70 -211 640]27943217492825389/135291469824 - (39500814611*α)/10436770529280 + (86539603*α^2)/10520264693514240
[48 -339 2400]27980586265125/1879048192 - (18242101*α)/9663676416 + (46325*α^2)/9740985827328
[36 -147 608]279102892371049/2818572288 - (1620520439*α)/217432719360 + (6305527*α^2)/219172181114880
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[28 -365 4768]27920832215838089/135291469824 - (36165846967*α)/10436770529280 + (132765431*α^2)/10520264693514240
[268 621 1440]27943217492825389/135291469824 - (39500814611*α)/10436770529280 + (86539603*α^2)/10520264693514240
[24 -339 4800]27980586265125/1879048192 - (18242101*α)/9663676416 + (46325*α^2)/9740985827328
[42 -141 480]279-14409464625/117440512 + (334313*α)/67108864 - (467*α^2)/22548578304
[20 -301 4544]279-19758072635963/135291469824 + (88791440773*α)/10436770529280 - (340140869*α^2)/10520264693514240
[98 237 576]279-44628862122469/67645734912 + (82264725851*α)/5218385264640 - (277169563*α^2)/5260132346757120
[18 -237 3136]27920832215838089/135291469824 - (36165846967*α)/10436770529280 + (132765431*α^2)/10520264693514240
[20 -109 608]2792603192368451/19327352832 - (71731980139*α)/10436770529280 + (32681021*α^2)/1502894956216320
[142 -426 1280]2847219362655/22020096 - (23616353*α)/1698693120 + (88609*α^2)/1712282664960
[142 -710 3552]284-748420289/22020096 - (2965889*α)/1698693120 + (8257*α^2)/1712282664960
[72 -362 1824]28414337348727/33030144 - (20095049*α)/2548039680 + (64777*α^2)/2568423997440
[72 -938 12224]2843168825391/5505024 - (5578769*α)/424673280 + (17617*α^2)/428070666240
[58 166 480]284-3168825391/5505024 + (5578769*α)/424673280 - (17617*α^2)/428070666240
[450 1046 2432]28414337348727/33030144 - (20095049*α)/2548039680 + (64777*α^2)/2568423997440
[6 26 160]284898876073/4128768 - (3328183*α)/318504960 + (11639*α^2)/321052999680
[58 -182 576]284-2515404965/33030144 + (13247899*α)/2548039680 - (52187*α^2)/2568423997440
[36 -74 160]284-7219362655/22020096 + (23616353*α)/1698693120 - (88609*α^2)/1712282664960
[36 -182 928]284-2515404965/33030144 + (13247899*α)/2548039680 - (52187*α^2)/2568423997440
[36 -362 3648]284-748420289/22020096 - (2965889*α)/1698693120 + (8257*α^2)/1712282664960
[36 -470 6144]284-898876073/4128768 + (3328183*α)/318504960 - (11639*α^2)/321052999680
[30 -154 800]284-898876073/4128768 + (3328183*α)/318504960 - (11639*α^2)/321052999680
[30 -214 1536]2847219362655/22020096 - (23616353*α)/1698693120 + (88609*α^2)/1712282664960
[30 -394 5184]284-2515404965/33030144 + (13247899*α)/2548039680 - (52187*α^2)/2568423997440
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[18 -38 96]2843168825391/5505024 - (5578769*α)/424673280 + (17617*α^2)/428070666240
[18 -74 320]2840
[18 -182 1856]28414337348727/33030144 - (20095049*α)/2548039680 + (64777*α^2)/2568423997440
[18 -218 2656]284-33350301073/33030144 + (53567663*α)/2548039680 - (170479*α^2)/2568423997440
[20 -86 384]284-33350301073/33030144 + (53567663*α)/2548039680 - (170479*α^2)/2568423997440
[20 -106 576]284898876073/4128768 - (3328183*α)/318504960 + (11639*α^2)/321052999680
[20 -246 3040]2840
[20 -266 3552]284-2515404965/33030144 + (13247899*α)/2548039680 - (52187*α^2)/2568423997440
[144 -1009 7072]287195681412081/2147483648 - (4212248873*α)/1159641169920 + (1509007*α^2)/166988328468480
[72 -1009 14144]2876516160299959/9663676416 - (83377332031*α)/5218385264640 + (37906889*α^2)/751447478108160
[78 -239 736]28711411367636139/19327352832 - (128891522963*α)/10436770529280 + (60051157*α^2)/1502894956216320
[48 -241 1216]287-4376582351905/9663676416 + (1390997701*α)/1043677052928 + (58861*α^2)/150289495621632
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[36 -433 5216]287-1899081549/67108864 + (182290871*α)/12079595520 - (101329*α^2)/1739461754880
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